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Simplifying x2 + 5x + -9 = 18 Reorder the terms: -9 + 5x + x2 = 18 Solving -9 + 5x + x2 = 18 Solving for variable 'x'. Reorder the terms: -9 + -18 + 5x + x2 = 18 + -18 Combine like terms: -9 + -18 = -27 -27 + 5x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -27 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 5x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 5x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 5x + x2 = 0 + 27 5x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 5x + x2 = 27 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 27 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 27 + 6.25 Combine like terms: 27 + 6.25 = 33.25 6.25 + 5x + x2 = 33.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + 2.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + 2.5 = 5.766281297 Simplifying x + 2.5 = 5.766281297 Reorder the terms: 2.5 + x = 5.766281297 Solving 2.5 + x = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5.766281297 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.766281297 + -2.5 x = 5.766281297 + -2.5 Combine like terms: 5.766281297 + -2.5 = 3.266281297 x = 3.266281297 Simplifying x = 3.266281297Subproblem 2
x + 2.5 = -5.766281297 Simplifying x + 2.5 = -5.766281297 Reorder the terms: 2.5 + x = -5.766281297 Solving 2.5 + x = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5.766281297 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.766281297 + -2.5 x = -5.766281297 + -2.5 Combine like terms: -5.766281297 + -2.5 = -8.266281297 x = -8.266281297 Simplifying x = -8.266281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.266281297, -8.266281297}
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